 where \(N={n\atopwithdelims ()2}\) . Moreover, the adjacency matrix \(A_n\)  of random graph of order \(n\)  is a random \(n\times n\)  real symmetric matrix whose upper-triangular entries \(\xi _{ij}\)  are bounded independent random variables which have mean \(\mu =p\)  and variance \(\sigma _p^2=p(1-p)\) . The diagonal elements of \(A_n\)  satisfy \(\nu =\mathbb {E}_{\mathcal {G}}[\xi _{ii}]=0\)  since loops are not permitted. The result by Füredi and Komlós [1]}, which we outline in Section REF , implies that w.h.p.,
\(|\lambda _1|=(n-1)p+1-p+O(n^{-1/2})=\big ( p+o(1)\big )n\) 
